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Received Oct 14, 2017; Accepted Feb 22, 2018
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1. Introduction
Reset options, whose strike price will be adjusted to a new strike price only on each of a set of prespecified dates if the stock price is below one of the reset levels, have greatly evolved in the past two decades. This reset clause embedded in derivative products can protect the investors amidst stock price declines. This makes a reset option useful in portfolio insurance (see, e.g., Boyle et al. [1]).
There are only a few articles studying the reset options in the academic literature. Gray and Whaley [2] were the first ones to examine the value of S & P 500 index bear market warrants with a periodic reset feature. In their other paper (see Gray and Whaley [3]), they provided an explicit formula for the reset option with a periodic reset date. Hsueh and Guo [4], on the other hand, analyzed the multiple reset feature that is included in most covered warrants traded in Taiwan. More recently, Cheng and Zhang [5] discussed the pricing and hedging of reset options and propose a closed-form pricing formula for this increasingly popular derivative instrument. Li et al. [6] derived a generalization of price formula for the reset call options with predetermined rates when the spot interest rate and volatility of stock are all time-dependent and deterministic. Liu et al. [7] evaluated the pricing of reset options when the underlying assets are autocorrelated. François-Heude and Yousfi [8] proposed a general valuation of reset option studied in Gray and Whaley [2] in which all options are replaced by ATM (At-The-Money) ones. Subsequent contributions include analytic extensions to multiple reset rights with shouting moment of Dai et al. [9, 10], Dai and Kwok [11], Yang et al. [12], and Goard [13], step (or snapshot)-reset design of Hsueh and Liu [14], and Yu and Shaw [15], average trigger reset clauses of Kao and Lyuu [16], Liao and Wang [17], Kim et al. [18], Chang et al. [19], Dai et al. [20], and Costabile et al. [21, 22], window reset option...